################BINOMIALE###### #P(X<=6),n=10,pi=0.2 F6<-pbinom(6,10,0.2) #P(36) s6<-1-pbinom(6,10,0.2) #°p(x>=6)=p(x>5) s5<-1-pbinom(5,10,0.2) #negbin p<-0.3 r<-3 #nx=5 fx=5-3=2 p2<-dnbinom(2,r,p) p2b<-pnbinom(2,r,p)-pnbinom(1,r,p) p1<-0.6 r1<-7 #nx>10 fx>10-7 P<-1-pnbinom(3,r1,p1) #nx= 7 fx=0 p0<-dnbinom(0,r1,p1) FR<-pnbinom(0:30,r1,p1) cbind((0:30)+r1,0:30,FR) #esercizio NEG1 ultima esercitazione r<-5 p<-0.1 #domanda a prob f_5<=10 pa<-pnbinom(10,r,0.1) pa #domanda b n_5<=10 #f_5= 10-5<=10-5 pb<-pnbinom(5,r,0.1) #esercizio NEG2 ultima esercitazione r<-21 p<-0.5 pA<-dnbinom(10,r,p) #esercizio NEG3 #r=1 #p=6/8 prob<-pnbinom(2,1,6/8) #esercizio 5.26 p<-6/8 r<-1 #f<4 pp<-pnbinom(2,1,6/8) ##########POISSON######################################### F6<-ppois(6,5) F64sx<-ppois(6,5)-ppois(4,5) F64c<-ppois(6,5)-ppois(3,5) p6<-dpois(6,5) #P(X>6) S6<-1-ppois(6,5) #ESERCIZIO 5 in esercizivariabilicasuali.pdf es1<-dpois(1,0.2*3)#una in 3 min es2<-1-ppois(1,0.2*5)#almeno 2 in 5 minuti es3<-ppois(1,0.2*15)#al massimo una in 15 minuti es3b<-dpois(0,0.2*15)+dpois(1,0.2*15) #ESERCIZIO 5 in esercizivariabilicasuali.pdf #a<-dpois(1,0.2*3) #b<-1-ppois(1,0.2*5) #c<-ppois(1,0.2*15) #ESERCIZIO 7 in esercizivariabilicasuali.pdf #p evento condizionate pd<-dpois(10,0.5*10) #p intersezione condizionato e condizionate pn<-dpois(9,0.3*10)*dpois(1,0.2*10) # p condizionata p<-pn/pd p #############NORMALE################################# FN<-pnorm(1.96) FN pnorm(1.96)-pnorm(1) mu<-10 sigma<-2 x<-12 FN2<-pnorm(12,10,2) FN2bis<-pnorm((12-10)/2) fpos<-1-pnorm(2) fneg<-pnorm(-2) #p(X<12,X>8) mu 10 sigma 2 Fint<-pnorm(12,10,2)- pnorm(8,10,2) Fintbis<-pnorm((12-10)/2)- pnorm((8-10)/2) z_0.99<-qnorm(0.99,0,1) x_0.99<-qnorm(0.99,5,2) xx_0.99b<-5+2*z_0.99 #ESERCIZIO N1 in esercizivariabilicasuali.pdf #a pa<-1-pnorm(6,5,sqrt(3)) pa_bis<-1-pnorm((6-5)/sqrt(3)) #b pb<-pnorm(7,5,sqrt(3))-pnorm(4,5,sqrt(3)) #ESERCIZIO N3 in esercizivariabilicasuali.pdf p1<-1-pnorm(110,100,5) p2<-pnorm(95,100,5) p3<-pnorm(110,100,5)-pnorm(95,100,5) ####approssimaione binomiale con normale standard n<-100 pi<-0.6 x<-65 z_65<-(65+0.5-100*0.6)/sqrt(100*0.6*0.4) P_65<-pnorm(z_65) P_65 Pesatto<-pbinom(65,100,0.6) z_64<-(64+0.5-100*0.6)/sqrt(100*0.6*0.4) p_65<-pnorm(z_65)-pnorm(z_64) pesatto<-dbinom(65,100,0.6) ########################### ########################### #relazioni gamma poisson ################################ #####lambda=1.5 tempo attesa 5 evento <=2################ POIS<-1-ppois(4,3) #uso poisson FGAM<-pgamma(2,5,1.5) #uso gamma #la probabilità che una gamma di par alpha (intero) #e lambda assuma valore <=x (tempo attesa) #è uguale alla prob che una poisson #di parametro lambda*x assuma valore >= di alpha #almeno alpha eventi in intervallo ampiezza x #####lambda=1 tempo attesa 5 evento <=2################ POIS<-1-ppois(4,2) #usopisson FGAM<-pgamma(2,5,1) #uso gamma ####lambda=2 tempo attesa 4 evento tra 3 e 5 POISL<-1-ppois(3,6) #3*2=6 POISU<-1-ppois(3,10) #5*2=10 P_3_5<-POISU-POISL P_3_H_gamma<-pgamma(5,4,2)-pgamma(3,4,2) #ESERCIZIO 1 in esercizivariabilicasuali.pdf #a con poisson a<-1-ppois(2,0.005*24) #a con gamma ag<-pgamma(24,3,0.005) #b con poisson b<-1-ppois(3,0.005*24) #b con gamma bg<-pgamma(24,4,0.005) #distribuzioni interesse statistico T 10 gdl x095<-qt(0.95,10) #distribuzioni interesse statistico chi2 10 gdl x095<-qchisq(0.95,10) #distribuzioni interesse statistico F 10 12 gdl x095<-qf(0.95,10,12) x05<-qf(0.05,12,10) 1/x095==x05